itemfit_bayesian: Bayesian parameter estimation of a test
In LatentREGpp: Item Response Theory Implemented in R and Cpp

Description Usage Arguments Model

Estimates the test parameters according to the Multidimensional Item Response Theory with bayesian adjust for dichotomous data

itemfit_bayesian(data, dim, model = "2PL", EMepsilon = 1e-04,
  clusters = NULL, quad_tech = NULL, quad_points = NULL,
  individual_weights = as.numeric(c()), initial_values = NULL,
  noguessing = TRUE, verbose = TRUE, save_time = TRUE)

`data`	The matrix containing the answers of tested individuals
`dim`	The dimensionality of the test
`model`	"1PL", "2PL" or "3PL"
`EMepsilon`	Convergence value to determine the accuracy of the test
`clusters`	A vector with cluster per dimension
`quad_tech`	A string with technique. "Gaussian" for Gaussian quadrature or "QMCEM" for Quasi-Monte Carlo quadrature. If NULL it's selected according to the model's dimension (QMCEM if dim>3).
`quad_points`	Amount of quadrature points. If quadratura_technique is "Gaussian". It can be NULL
`individual_weights`	A vector with Weights of the quadrature points.
`initial_values`	A matrix with initial values for estimation process. Be sure about dimension, model and consistency with data.
`noguessing`	In 3PL model and dimension is greater than 1, If true, guessing parameter will not be estimated in zeta vector. Instead c value will have a default initial value. Otherwise guessing parameter will be estimated with zeta vector.
`verbose`	True for get information about estimation process in runtime. False in otherwise.
`save_time`	True for save estimation time. False otherwise.

Bayesian model is based in itemfit models. It has a Q_{i} function to optimize according parameters like in itemfit. However this model is given by:

Q_{i} = N * log(P_{ζ_{i}}(ζ_{i})) + \hat{Q_{i}}

Where i index is referenced for items in test.

Then, log posterior is given by:

log(P_{ζ_{i}}(ζ_{i})) = - \frac{N}{2} (\frac{(a_{1i} - μ_{a1i})^2}{σ_{1i}^2} + \cdots + \frac{(a_{Di} - μ_{aDi})^2}{σ_{Di}^2} + \frac{(d_{i} - μ_{di})^2}{σ_{di}^2} + \frac{(c_{i} - μ_{ci})^2}{σ_{ci}^2})

Where a,d and c are parameters, D is the dimension of test. You can give the μ values for each parameters through initial values matrix. In otherwise μ will have default initial values value σ^2 values are constant σ_a^2 = 0.64, σ_d^2 = 4, σ_c^2 = 0.009